Insurance may be defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for a premium. It may additionally be thought of as a guaranteed and known small loss to prevent or mitigate a large, possibly devastating loss. Insurance companies offer and individuals purchase insurance contracts based on their understanding of the consequences of certain events and the likelihood that the events will occur. For example, it is rare for homes to be consumed by fire, but it is common to obtain home insurance to cover the catastrophic risk that a home will be destroyed by fire. The more likely the risk, the more expensive the home insurance will be. In addition, the less expensive the house, the less expensive the home insurance will be.
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Statistics also provides tools for prediction and forecasting using data and statistical models. Models are developed to explain behavior or to make predictive forecasts for a group of individuals or items (also known as a population). A model of a system may be defined by a set of variables. For example, when a financial institution creates a new mortgage offering, it may create a model of the market in which the product is expected to be offered to project demand for the mortgage offering. Model variables may include features of the potential customer base (such as income or demographics), competition, expected customer behavior (such as prepayment assumptions), interest rates, and market behavior. The model may produce an outcome comprising an objective projection (such as an expected annual earning from the product) or a subjective projection (such as the likelihood of obtaining a pre-selected annual earning of the product). Stochastic models (or models that test a system with different fact patterns known as scenarios or “what-if” scenarios) produce sets of outcomes, with each outcome based on a different scenario. Stochastic modeling outcomes may comprise a set of likelihoods of an event, with each likelihood corresponding to a scenario. Scenarios constructed to model demand for the mortgage offering may differ in the features of the offering, such as types of prepayment options or amounts of interest rates. Scenarios may also differ in prepayment assumption or interest rate market conditions in which the product is to be offered, such as an inflationary or recessionary economy or the number of, or similarity of competing products. Examples of scenario parameter values include default assumptions on mortgage payments, and expected returns and volatility parameters for the underlying distribution of market performance. Scenarios may be constructed with a mix of some or all of the variables that make up the model.
Thus, stochastic modeling (or modeling of scenarios, some more probable than others) is performed using data from the population to explain system changes due to the differences between scenarios. Each scenario may be defined at least in part by the set of model variables, and scenario data for each of the scenarios may comprise at least some parameter values for the set of variables such that, when data for a scenario are inputted into the model, the model may produce a different model outcome.
Examples of stochastic processes that may be modeled include stock market and exchange rate fluctuations; signals such as speech, audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks.
In the context of insurance, the group under analysis may be the population of insurance policyholders models, and models may be developed to quantify risk or exposure for certain liabilities for the population of insurance policyholders or to estimate requirements of an insurance company for the levels of capital and asset reserves that will be required to support a series of insurance policies being modeled. Variables for such insurance related models may include mortality assumptions, lapse behavior (such as the rate at which insurance policies are expected to lapse), as well as investment assumptions like interest rate and market behavior. The model outcomes may comprise measures of a risk comprising a likelihood of an occurrence of the insurance liability for a scenario. Variables in a scenario in the insurance context include mortality assumptions, an insurance policy lapse rate, and a rate of market return for investment oriented insurance products. Examples of scenario parameter values include a selected mortality rate, a selected lapse rate, and a selected rate of market return, with the selected rates being modified across scenarios to test the effect of rate changes on the model outcome. Stochastic modeling of risk scenarios may be performed to identify changes in the risk or exposure that may occur or the subsequent impact on future cashflows, capital and reserving requirements, given different scenarios.
Typically, commercial actuarial models of insurance liabilities are developed based on the entire population of insurance policyholders, and stochastic modeling of risk scenarios is performed using the entire population. Analyzing risk scenarios with the entire population eliminates sampling error and therefore may provide more exact information than analyzing risk scenarios based on a random sample of contracts. However, modeling with the entire population is computationally complex and time consuming, despite advances in technology, limiting the number of risk scenarios that can be tested and making it hard to adequately assess risk in real time.
Analyzing risk scenarios with only a subset of the entire dataset may reduce computational time for complex financial calculations involving the use of stochastic scenarios. However, modeling with only a subset of the available data may not provide results that are accurate to an acceptable tolerance level.